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Chaotic linear system solvers in a variable-grain data-driven multiprocessor system

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PARLE '91 Parallel Architectures and Languages Europe (PARLE 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 506))

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Abstract

Linear systems are important problems in many scientific applications. While asynchronous methods are effective solutions to linear systems, they are difficult to realize due to the chaotic behavior of the algorithms. In this paper, we investigate the implementation as well as the performance of an asynchronous method, namely chaotic relaxation, in our Variable-grain Tagged-Token Data-flow (VTD) System. We compare asynchronous methods with synchronous methods executed on both the fine-grain and the coarse-grain execution models. New high-level data-flow language constructs are introduced in order to express asynchronous operations. A new firing rule that deviates from the single assignment rule of functional languages is proposed to support the implementation of asynchronous computations in the VTD system. In addition to the conventional speedup measure, we then define new performance measurements, called Growth Factor, Scalability Factor, and Robustness to characterize the system performance from the machine and application viewpoints. Simulation results indicate that asynchronous methods are more efficient than synchronous methods and that the coarse-grain execution mode is more efficient that the fine-grain execution mode in our VTD system.

This material is based upon work supported in part by the U.S. Department of Energy, Department of Energy Research, under Grant No. DE-FG03-87ER25043.

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Emile H. L. Aarts Jan van Leeuwen Martin Rem

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© 1991 Springer-Verlag

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Gaudiot, JL., Lin, CM. (1991). Chaotic linear system solvers in a variable-grain data-driven multiprocessor system. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds) PARLE '91 Parallel Architectures and Languages Europe. PARLE 1991. Lecture Notes in Computer Science, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54152-7_73

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  • DOI: https://doi.org/10.1007/3-540-54152-7_73

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54152-3

  • Online ISBN: 978-3-540-47472-2

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